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find the side of the Pentagon as usual
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before watching try to solve this
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problem yourself first we Mark the
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vertices of the Pentagon for example
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with the letters a b c d and e next we
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extend the sides of the Pentagon a e and
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D to form a rectangle like this the
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fourth vertex of the resulting rectangle
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is marked for example as F considering
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that the opposite sides of the rectangle
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are equal AF will be equal to D and
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equal to 12 and DF will be equal to AE
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and equal to 15 next we connect the
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points A and C as a result we get two
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right triangles with a common hypotenuse
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AC from the right triangle AFC we apply
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the Pythagorean theorem the square of
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the hypotenuse AC will be equal to the
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sum of the squares of the legs AF and CF
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let's calculate the square of the
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hypotenuse AC we substitute 12 for AF
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and for CF we substitute FD plus DC that
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is we add 15 and 14 to get 29 squaring
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841 and squaring 12 gives us 144 adding
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985 next we apply the Pythagorean
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theorem for the triangle ABC to express
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the desired side BC of the Pentagon the
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sum of the squares of the sides BC and
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ab will be equal to the square of the
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hypotenuse AC therefore for bc^ 2 will
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be equal to ac^ 2 minus ab^ 2 we
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substitute the known sides and calculate
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the squares ac^ squ is
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256 subtracting we get
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729 therefore the side BC denoted by X
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will be equal to the square < TK of
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729 that is X = 27 we write the final
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answer the unknown side of the Pentagon
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in the figure is equal to 27 the task is
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solved if you understand the solution
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give it a like leave comments and as
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usual subscribe to the channel and I
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will see you in the next video
